Mafunso a Zitsanzo ndi Kukambirana za Kuchotsa Vector
Pendauluan
Mu masamu ndi fizikisi, ma vector ndi lingaliro lofunikira lomwe limagwiritsidwa ntchito pofotokoza zochitika zambiri zachilengedwe ndi zaukadaulo. Vector ndi kuchuluka komwe kuli ndi kukula ndi njira. Zitsanzo zina zofunika za ma vector ndi kusamuka, liwiro, kuthamanga, ndi mphamvu. M'nkhaniyi, tikambirana za kuchotsa ma vector, ngakhale kuti nkhaniyi nthawi zambiri imagogomezeredwa pankhani yophatikiza ma vector.
Kuchotsa mavekesi ndi ntchito yofunika kwambiri pakuwunika mavekesi. Kuti tidziwe bwino mfundo imeneyi, tiyeni tiwone zitsanzo za mavuto ndi zokambirana zokhudzana ndi kuchotsa mavekesi.
Kuchotsa Vekitala
Kuchotsa vekitala {\displaystyle \mathbf{A} – \mathbf{B}} kumatanthauzidwa ngati ntchito yowonjezera vekitala {\displaystyle \mathbf{A}} ndi vekitala {\displaystyle -\mathbf{B}}, pomwe {\displaystyle -\mathbf{B}} ndi vekitala yokhala ndi kukula kofanana ndi {\displaystyle \mathbf{B}} koma yosiyana. Mwa masamu, izi zitha kulembedwa motere:
{\chiwonetsero \mathbf{A} - \mathbf{B} = \mathbf{A} + (-\mathbf{B})}
Mafunso ndi Kukambirana Zitsanzo
Funso 1: Kuchotsa Ma Vector a Miyeso Iwiri
Tiyerekeze kuti pali ma vector awiri mu ma coordinates a Cartesian:
{\displaystyle \mathbf{A} = (4, 3)} ndi {\displaystyle \mathbf{B} = (1, 2)}. Koperani {\displaystyle \mathbf{A} – \mathbf{B}}.
Kukambirana:
Gawo loyamba ndikupeza vekitala yoyipa ya {\displaystyle \mathbf{B}}, yomwe ndi:
{\displaystyle -\mathbf{B} = (-1, -2)}
Kenako, onjezani vekitala {\displaystyle \mathbf{A}} ndi {\displaystyle -\mathbf{B}}:
{\mawonekedwe \mathbf{A} - \mathbf{B} = (4, 3) + (-1, -2)}
Chitani kuwonjezera kwa vekitala powonjezera gawo lililonse la x ndi y:
{\mawonekedwe \mathbf{A} - \mathbf{B} = (4 + (-1), 3 + (-2))}
{\mawonekedwe \mathbf{A} - \mathbf{B} = (3, 1)}
Kotero, zotsatira za kuchotsa ma vector {\displaystyle \mathbf{A} – \mathbf{B}} ndi vector (3, 1).
Funso 2: Kuchotsa Ma Vector a Magawo Atatu
Popeza ma vector awiri ali mu ma coordinates atatu-dimensional:
{\displaystyle \mathbf{P} = (2, -4, 6)} ndi {\displaystyle \mathbf{Q} = (-3, 5, 7)}. Koperani {\displaystyle \mathbf{P} – \mathbf{Q}}.
Kukambirana:
Gawo loyamba ndikupeza vekitala yoyipa ya {\displaystyle \mathbf{Q}}:
{\displaystyle -\mathbf{Q} = (3, -5, -7)}
Kenako, onjezani vekitala {\displaystyle \mathbf{P}} ndi {\displaystyle -\mathbf{Q}}:
{\mawonekedwe \mathbf{P} - \mathbf{Q} = (2, -4, 6) + (3, -5, -7)}
Chitani kuwonjezera kwa vekitala powonjezera gawo lililonse la x, y, ndi z:
{\mawonekedwe \mathbf{P} - \mathbf{Q} = (2 + 3, -4 + (-5), 6 + (-7))}
{\mawonekedwe \mathbf{P} - \mathbf{Q} = (5, -9, -1)}
Kotero, zotsatira za kuchotsa ma vector {\displaystyle \mathbf{P} – \mathbf{Q}} ndi vector (5, -9, -1).
Funso 3: Kuchotsa Vekitala mu Dongosolo Lovuta
Tiyerekeze kuti pali ma vekitala awiri omwe akuimiridwa ndi manambala ovuta:
{\displaystyle \mathbf{M} = 3 + 4i} ndi {\displaystyle \mathbf{N} = 1 + 2i}. Koperani {\displaystyle \mathbf{M} – \mathbf{N}}.
Kukambirana:
Gawo loyamba ndikupeza vekitala yoyipa ya {\displaystyle \mathbf{N}}:
{\mawonekedwe -\mathbf{N} = -1 – 2i}
Kenako, onjezani vekitala {\displaystyle \mathbf{M}} ndi {\displaystyle -\mathbf{N}}:
{\mawonekedwe \mathbf{M} – \mathbf{N} = (3 + 4i) + (-1 – 2i)}
Chitani kuwonjezera kwa vekitala powonjezera gawo lililonse lenileni komanso longopeka:
{\mawonekedwe \mathbf{M} – \mathbf{N} = (3 + (-1)) + (4i + (-2i))}
{\mawonekedwe \mathbf{M} - \mathbf{N} = 2 + 2i}
Kotero, zotsatira za kuchotsa ma vector {\displaystyle \mathbf{M} – \mathbf{N}} ndi nambala yovuta 2 + 2i.
Funso 4: Kuchotsa Vector mu Polar Coordinate System
Tiyerekeze kuti pali ma vector awiri mu polar coordinates:
{\displaystyle \mathbf{U}} ili ndi kukula kwa 5 ndi ngodya ya 30°,
ndipo {\displaystyle \mathbf{V}} ili ndi kukula kwa 3 ndi ngodya ya 150°.
Kuwerengera {\displaystyle \mathbf{U} – \mathbf{V}}.
Kukambirana:
Gawo loyamba ndikusintha ma vector {\displaystyle \mathbf{U}} ndi {\displaystyle \mathbf{V}} kukhala ma Cartesian coordinates.
Za {\displaystyle \mathbf{U}}:
{\displaystyle U_x = 5 \cos(30^\circ) = 5 \left(\frac{\sqrt{3}}{2}\right) = 5 \cdot 0.866 = 4.33}
{\displaystyle U_y = 5 \sin(30^\circ) = 5 \left(\frac{1}{2}\right) = 5 \cdot 0.5 = 2.5}
Kotero {\displaystyle \mathbf{U}} mu Cartesian ndi (4.33, 2.5).
Za {\displaystyle \mathbf{V}}:
{\displaystyle V_x = 3 \cos(150^\circ) = 3 \left(\frac{-\sqrt{3}}{2}\right) = 3 \cdot (-0.866) = -2.598}
{\displaystyle V_y = 3 \sin(150^\circ) = 3 \left(\frac{1}{2}\right) = 3 \cdot 0.5 = 1.5}
Kotero {\displaystyle \mathbf{V}} mu Cartesian ndi (-2.598, 1.5).
Gawo lotsatira, werengerani kuchotsa kwa vekitala mu Cartesian:
{\displaystyle \mathbf{U} – \mathbf{V} = (4.33, 2.5) – (-2.598, 1.5)}
Izi zikutanthauza powonjezera negative ya vekitala:
{\displaystyle \mathbf{U} – \mathbf{V} = (4.33 + 2.598, 2.5 – 1.5)}
{\displaystyle \mathbf{U} – \mathbf{V} = (6.928, 1)}
Kotero, zotsatira za kuchotsa vekitala {\displaystyle \mathbf{U} – \mathbf{V}} mu ma coordinates a Cartesian ndi (6.928, 1).
Mapeto
Kuchotsa mavekitala ndi ntchito yofunika kwambiri ya masamu m'magawo ambiri omwe amagwiritsa ntchito kusanthula mavekitala. Kaya mu machitidwe a ma coordinate a magawo awiri, atatu, ovuta, kapena a polar, mfundo yoyambira imakhalabe yofanana: kuwonjezera vekitala imodzi ku negative ya ina. Zitsanzo zomwe zili pamwambapa zikuwonetsa njira zosiyanasiyana zogwiritsira ntchito ntchitoyi m'malo osiyanasiyana, kutithandiza kumvetsetsa lingalirolo mozama komanso moyenera.
